A Function $\mathrm { f } ( \mathrm { x } )$

Multiple Choice

A function $\mathrm { f } ( \mathrm { x } )$ , a point $\mathrm { c }$ , the limit of $\mathrm { f } ( \mathrm { x } )$ as $x$ approaches $\mathrm { c }$ , and a positive number $\varepsilon$ is given. Find a number $\delta > 0$ such that for all $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $$f ( x ) = \sqrt { 58 - 3 x } , c = - 2 , \varepsilon = 0.2$$

A) $L = 8 ; \delta = 1.08$
B) $L = 9 ; \delta = 1.05$
C) $L = j - 7 ; \delta = 0.52$
D) $\mathrm { L } = 8 ; \delta = 1.05$